The sum of two numbers is $113$, and their difference is $5$. What are the two numbers?
Explanation: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 113}$ ${x-y = 5}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 118 $ $ x = \dfrac{118}{2} $ ${x = 59}$ Now that you know ${x = 59}$ , plug it back into $ {x+y = 113}$ to find $y$ ${(59)}{ + y = 113}$ ${y = 54}$ You can also plug ${x = 59}$ into $ {x-y = 5}$ and get the same answer for $y$ ${(59)}{ - y = 5}$ ${y = 54}$ Therefore, the larger number is $59$, and the smaller number is $54$.